LESSON 9–3 Rotations

Five-Minute Check (over Lesson 9–2) TEKS Then/Now New Vocabulary Key Concept: Rotation Example 1: Draw a Rotation Key Concept: Rotations in the Coordinate Plane Example 2: Rotations in the Coordinate Plane Example 3: Rotations in the Coordinate Plane Lesson Menu

Find the coordinates of the figure under the given translation Find the coordinates of the figure under the given translation. RS with endpoints R(1, –3) and S(–3, 2) along the translation vector 2, –1 ___ A. R'(–2, –2), S'(–1, 1) B. R'(0, –3), S'(–5, 3) C. R'(3, –4), S'(–1, 1) D. R'(3, –4), S'(–5, 3) 5-Minute Check 1

Find the coordinates of the figure under the given translation Find the coordinates of the figure under the given translation. ΔABC with vertices A(–4, 3), B(–2, 1), and C(0, 5) under the translation (x, y) → (x + 3, y – 4) A. A'(–2, 1), B'(1, –3), C'(3, –1) B. A'(–1, –1), B'(1, –3), C'(3, 1) C. A'(0, 5), B'(–6, 3), C'(4, 7) D. A'(1, –1), B'(2, 5), C'(5, 9) 5-Minute Check 2

Find the coordinates of the figure under the given translation Find the coordinates of the figure under the given translation. trapezoid LMNO with vertices L(2, 1), M(5, 1), N(1, –5) and O(0, –2) under the translation (x, y) → (x – 1, y + 4) A. L'(1, 5), M'(4, 5), N'(0, –1), O'(–1, 2) B. L'(2, 6), M'(5, 7), N'(1, 0), O'(0, 3) C. L'(3, –3), M'(6, –2), N'(0, –8), O'(–1, –6) D. L'(4, –4), M'(7, 5), N'(0, –1), O'(1, 4) 5-Minute Check 3

Find the translation that moves AB with endpoints A(2, 4) and B(–1, –3) to A'B' with endpoints A'(5, 2) and B'(2, –5). ___ ____ A. (x – 2, y – 3) B. (x + 2, y + 2) C. (x – 3, y + 2) D. (x + 3, y – 2) 5-Minute Check 4

The preimage of rectangle ABCD has vertices at A(–4, 5), B(–4, –3), C(1, –3), and D(1, 5). Its image has vertices at A'(–1, 3), B'(–1, –5), C'(4, –5), and D'(4, 3). Write the ordered pair that describes the transformation of the rectangle. A. (x, y) → (x + 3, y – 2) B. (x, y) → (x – 3, y + 2) C. (x, y) → (x + 2, y + 3) D. (x, y) → (x – 2, y – 3) 5-Minute Check 5

Mathematical Processes G.1(E), G.1(G) Targeted TEKS G.3(A) Describe and perform transformations of figures in a plane using coordinate notation. Mathematical Processes G.1(E), G.1(G) TEKS

Draw rotations in the coordinate plane. You identified rotations and verified them as congruence transformations. Draw rotations. Draw rotations in the coordinate plane. Then/Now

center of rotation angle of rotation Vocabulary

Concept

Rotate quadrilateral RSTV 45° counterclockwise about point A. Draw a Rotation Rotate quadrilateral RSTV 45° counterclockwise about point A. Draw a segment from point R to point A. Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR. Locate point R' so that AR = AR'. Repeat this process for points S, T, and V. Connect the four points to form R'S'T'V'. Example 1

Draw a Rotation Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A. Answer: Example 1

For the diagram, which description best identifies the rotation of triangle ABC around point Q? A. 20° clockwise B. 20° counterclockwise C. 90° clockwise D. 90° counterclockwise Example 1

Concept

First, draw ΔDEF and plot point G. Rotations in the Coordinate Plane Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 115° clockwise about the point G(–4, –2). First, draw ΔDEF and plot point G. Draw a segment from point G to point D. Use a protractor to measure a 115° angle clockwise with as one side. Draw Use a compass to copy onto Name the segment Repeat with points E and F. Example 2

Rotations in the Coordinate Plane Answer: ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G. Example 2

Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6) Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1). A. B. C. D. Example 2

Rotations in the Coordinate Plane Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin? A (5, –3) B (–5, –3) C (–3, 5) D (3, –5) Example 3

Answer: The answer is C, (–3, 5). Rotations in the Coordinate Plane Read the Item You are given a graph of hexagon DGJTSR and asked to identify the coordinates of the image of point T after a 90° counterclockwise rotation about the origin. Solve the Item To find the coordinates of point T after a 90 counterclockwise rotation about the origin, multiply the y-coordinate by –1 and then interchange the x- and y-coordinates. (x, y) → (–y, x) (5, 3) → (–3, 5) Answer: The answer is C, (–3, 5). Example 3

Triangle PQR is shown below Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin? A. (–5, –4) B. (–5, 4) C. (5, 4) D. (4, –5) Example 3

LESSON 9–3 Rotations